Start with volume of cone equation
V = (pi)*r^2*(h/3)
Known values
V = 47 in^3 and r = 3 in
Solve for h
h = 3*(V/((pi)*r^2))
h = 4.99 in
Since this is the height for only one cone it would need to be doubled since two (2) cones make an hourglass.
Therefore total height would be approximately 9.98 inches. Suggest to make it 10.0 inches due to some transitional length were the cones come together in the middle
